A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Generative model synthesizes complex data structures with composite and nested types.
Proposes a new model for clustering multiplex networks with compositional data.
We derive explicit valuation formulae for an exotic path-dependent interest rate derivative, namely an option on the composition of LIBOR rates. The formulae are based on Fourier transform methods for option pricing. We consider two models for the evolution of interest rates: an HJM-type forward rate model and a LIBOR-…
Develops methods for causal inference in compositional data using instrumental variables.
Connected sum and trivalent vertex sum are natural operations on genus 2 spatial graphs and, as with knots, tunnel number behaves in interesting ways under these operations. We prove sharp Scharlemann-Schultens type bounds for the tunnel number of a composite genus 2 spatial graph. For the tunnel number of a composite …
New samplers improve compositional generation with diffusion models.
Study causal effects on humans in mixed human-AI systems with unobserved unit types.
Let be a tunnel number two knot. Then, by considering the -decompositions, is one of (3, 0)-, (2, 1)-, (1, 2)- or (0, 3)-knots. In the present paper, we analyze the connected sum summands of composite tunnel number two knots and give a complete table of those summands from the point of view of -…
A folded type model is developed for analyzing compositional data. The proposed model involves an extension of the -transformation for compositional data and provides a new and flexible class of distributions for modeling data defined on the simplex sample space. Despite its rather seemingly complex structure, emplo…
In this paper, we investigate the properties of the full colored HOMFLYPT invariants in the full skein of the annulus . We show that the full colored HOMFLYPT invariant has a nice structure when . The composite invariant is a combination of the full colored HOMFLYPT invariants. In order to …
This paper studies neural network operators and their convergence properties.
Data augmentation improves microbiome disease prediction.
Several formulas for computing coarse indices of twisted Dirac type operators are introduced. One type of such formulas is by composition product in -theory. The other type is by module multiplications in -theory, which also yields an index theoretic interpretation of the duality between Roe algebra and stable Hi…
New algorithm solves complex optimization problems without needing projections.
Network embedding has proved extremely useful in a variety of network analysis tasks such as node classification, link prediction, and network visualization. Almost all the existing network embedding methods learn to map the node IDs to their corresponding node embeddings. This design principle, however, hinders the ex…
We define composite DAHA-superpolynomials of torus knots, depending on pairs of Young diagrams and generalizing the composite HOMFLY-PT polynomials in the theory of the skein of the annulus. We provide various examples. Our superpolynomials extend the DAHA-Jones (refined) polynomials and satisfy all standard symmetries…
Dual averaging-type methods are widely used in industrial machine learning applications due to their ability to promoting solution structure (e.g., sparsity) efficiently. In this paper, we propose a novel accelerated dual-averaging primal-dual algorithm for minimizing a composite convex function. We also derive a stoch…
New methods convert complex link presentations to simpler, recognizable forms.
Our objective is to estimate the unknown compositional input from its output response through an unknown system after estimating the inverse of the original system with a training set. The proposed methods using artificial neural networks (ANNs) can compete with the optimal bounds for linear systems, where convex optim…
New infinite-type loxodromic elements found in surface mapping classes.
Donor-aware scRNA-seq benchmarks improve classification accuracy in inflammatory bowel disease.
In this paper we construct proper biharmonic submanifolds into various types of ellipsoids. We also prove, in this context, some useful composition properties which can be used to produce large families of new proper biharmonic immersions.
Paper introduces a new index to measure financial and workplace resilience of firms.
Unified SGD method improves convergence for nested optimization problems.
New financial ratios using compositional data improve analysis of firm health.
We generalize Newton-type methods for minimizing smooth functions to handle a sum of two convex functions: a smooth function and a nonsmooth function with a simple proximal mapping. We show that the resulting proximal Newton-type methods inherit the desirable convergence behavior of Newton-type methods for minimizing s…
The successful application of general reinforcement learning algorithms to real-world robotics applications is often limited by their high data requirements. We introduce Regularized Hierarchical Policy Optimization (RHPO) to improve data-efficiency for domains with multiple dominant tasks and ultimately reduce require…
We study the meromorphic open-string vertex algebras and their modules over the two-dimensional Riemannian manifolds that are complete, connected, orientable, and of constant sectional curvature . Using the parallel tensors, we explicitly determine a basis for the meromorphic open-string vertex algebra, its mo…
Bayesian modeling predicts hydroxide ion conductivity in polymer membranes.
We introduce a special class of nilpotent Lie groups of step 2, that generalizes the so called (eisenberg)-type groups, defined by A. Kaplan in 1980. We change the presence of inner product to an arbitrary scalar product and relate the construction to the composition of quadratic forms. We present the geodesic equat…
We consider the sectoral composition of a country's GDP, i.e. the partitioning into agrarian, industrial, and service sectors. Exploring a simple system of differential equations we characterize the transfer of GDP shares between the sectors in the course of economic development. The model fits for the majority of coun…
We present a construction of cellular BF theory (in both abelian and non-abelian variants) on cobordisms equipped with cellular decompositions. Partition functions of this theory are invariant under subdivisions, satisfy a version of the quantum master equation, and satisfy Atiyah-Segal-type gluing formula with respect…
The study broadens the concept of cyclic polytopes to Veronese polytopes.
As deep neural networks become more adept at traditional tasks, many of the most exciting new challenges concern multimodality---observations that combine diverse types, such as image and text. In this paper, we introduce a family of multimodal deep generative models derived from variational bounds on the evidence (dat…
Federated learning (FL) has recently emerged as a new form of collaborative machine learning, where a common model can be learned while keeping all the training data on local devices. Although it is designed for enhancing the data privacy, we demonstrated in this paper a new direction in inference attacks in the contex…
In this paper, we unify the Markov theory of a variety of different types of graphs used in graphical Markov models by introducing the class of loopless mixed graphs, and show that all independence models induced by -separation on such graphs are compositional graphoids. We focus in particular on the subclass of rib…
Construction of (colored) knot polynomials for double-fat graphs is further generalized to the case when "fingers" and "propagators" are substituting R-matrices in arbitrary closed braids with m-strands. Original version of arXiv:1504.00371 corresponds to the case m=2, and our generalizations sheds additional light on …
We propose a new stochastic first-order algorithmic framework to solve stochastic composite nonconvex optimization problems that covers both finite-sum and expectation settings. Our algorithms rely on the SARAH estimator introduced in (Nguyen et al, 2017) and consist of two steps: a proximal gradient and an averaging s…
This work is an analytical and numerical study of the composition of several fractals into one and of the relation between the composite dimension and the dimensions of the component fractals. In the case of composition of standard IFS with segments of equal size, the composite dimension can be expressed as a function …
Transformers learn to generalize unseen tasks by composing self-attention layers.
We consider smooth bounded surfaces with a smooth boundary and a prescribed background metric g_0. We now consider all metrics g conformal to g_0 which have a prescribed volume M. We now minimize the first eigenvalue of the Laplace operator of g over the metrics conformal to g_0 and having the prescribed volume. We sho…
New geometric approach for analyzing compositional data like gut microbiomes.
We prove a classification theorem for conformal maps with respect to the control distance generated by a system of diagonal vector fields. It turns out that all such maps can be obtained as compositions of suitable dilations, inversions and isometries. We also classify all umbilical surfaces of the underlying metric.
Study on deep neural networks using branching processes and Mehler's formula.
The increasing richness in volume, and especially types of data in the financial domain provides unprecedented opportunities to understand the stock market more comprehensively and makes the price prediction more accurate than before. However, they also bring challenges to classic statistic approaches since those model…
Generative processes in biology and other fields often produce data that can be regarded as resulting from a composition of basic features. Here we present an unsupervised method based on autoencoders for inferring these basic features of data. The main novelty in our approach is that the training is based on the optim…
Fast detection of changepoints in linear regression models.
We establish conditions for compositional generalization in machine learning.